I live on Vancouver Island, where it rains from October to April or so, and I run outside year round.
I agree that it seems impossible to find GoreTex that also breathes, however I must say that Arc'teryx recently released the best running jacket ever. I had a chance to test this jacket last winter (pre-release) and based on that, was happy to pay the $350 price tag to buy one of my own this fall. It breathes incredibly well considering the level of waterproofing, in part due to the venting under the arms.
http://arcteryx.com/product.aspx?language=EN&gender=mens&model=Norvan-Jacket
Personally, I accept that most rain jackets are not waterproof, and I've tried many jackets over the years. By far my favorite before the new Norvan I linked above (I have been using for over 3 years) is the Arc'Teryx Incendo. The Incendo weighs only 130 grams, has an integrated hood, and stuffs into its own pocket when not needed. Ive run hundreds and hundreds of hours in miserable weather, and it is fantastic. For me, it works in weather to just around the freezing point (which can be improved of course by layering under the jacket). This jacket is NOT waterproof. I accept that I will be wet. But it keeps me warm and so that is all that matters. Keeps out wind, allows to trap some temperature. It is great.
http://arcteryx.com/product.aspx?language=EN&gender=mens&model=Incendo-Hoody
So now that I own BOTH jackets, I still wear the Incendo more often than the waterproof Norvan. I bust out the Norvan when it is a combination of more than one of the following: close to freezing, very windy, torrential rain, below freezing. So $350 is a high price for a secondary jacket, but when the conditions warrant it, there is no rival.